The invention is based on a fuel injection pump as defined hereinafter. A pump of this kind is known from German Patent Application DE-OS 39 12 624, U.S. Pat. No. 5,085,196. There, a diversion by the feed pump is prevented via hydraulically locking the feed pump pressure control valve, so that all the fuel fed is used to build up the control pressure. In this way, even when the engine is cold, a high suction chamber pressure and the associated adjustment of injection toward "early" can be attained as fast as possible. The known cold starting system comprises a fuel injection pump having an injection adjuster, a feed pump by way of which a pressure control valve, located in the incoming line to the fuel injection pump, controls the inflow to the suction chamber, and two valves disposed parallel in the relief line of the pressure control valve restoring chamber, one of which valves is opened as a function of the engine operating temperature, and the other of which is opened as a function of the control pressure in the suction chamber. In the warmup phase or upon engine starting, these two valves in the relief line of the pressure control restoring chamber make possible a diversion of the fuel inflow by hydraulically blocking the bypass line via the pressure control valve, so that all the fuel flows to the fuel injection pump, and in a known manner can rapidly build up the control pressure, which results in an adjustment of the injection adjuster toward "early". This special adjustment toward "early" is cancelled when a certain pressure and the associated opening of the pressure valve is attained or at the end of the warmup phase by opening of the pressure holding valve; the relief line of the restoring chamber of the pressure control valve is thereupon opened. After that, the pressure acting upon the injection adjuster is controlled in a known manner as a function of rpm by the pressure control valve. The adjustment toward "early" improves the cold starting performance and the operation of the engine in the warmup phase. A disadvantageous feature of the known apparatus is the complicated additional disposition of the pressure valves in the relief line of the feed pump pressure control valve, which requires additional space and is therefore more expensive. This is why there is a need for a simplified structure of the entire cold starting device for an internal combustion engine.